diff --git a/experimental/LieAlgebras/test/WeylGroup-test.jl b/experimental/LieAlgebras/test/WeylGroup-test.jl
index a87701a7958..bd2f8aa3fb3 100644
--- a/experimental/LieAlgebras/test/WeylGroup-test.jl
+++ b/experimental/LieAlgebras/test/WeylGroup-test.jl
@@ -112,9 +112,15 @@ include(
             if is_finite(W) # remove once rand(W) is implemented for infinite groups
               w = rand(W)
               @test w == inv(iso)(iso(w))
+              v = rand(W)
+              @test iso(v*w) == iso(v)*iso(w)
+              @test v*w == inv(iso)(iso(v)*iso(w))
             end
             g = rand_pseudo(G)
             @test g == iso(inv(iso)(g))
+            h = rand_pseudo(G)
+            @test inv(iso)(h*g) == inv(iso)(h)*inv(iso)(g)
+            @test h*g == iso(inv(iso)(h)*inv(iso)(g))
           end
         end
       end
@@ -144,9 +150,15 @@ include(
                 if is_finite(W) # remove once rand(W) is implemented for infinite groups
                   w = rand(W)
                   @test w == inv(iso)(iso(w))
+                  v = rand(W)
+                  @test iso(v*w) == iso(v)*iso(w)
+                  @test v*w == inv(iso)(iso(v)*iso(w))
                 end
                 g = rand_pseudo(G)
                 @test g == iso(inv(iso)(g))
+                h = rand_pseudo(G)
+                @test inv(iso)(h*g) == inv(iso)(h)*inv(iso)(g)
+                @test h*g == iso(inv(iso)(h)*inv(iso)(g))
               end
             end
           end